鞅论

Jensen不等式在鞅论中的应用

The Application of Jensen 's Inequality in Martingale 's Theories

讨论了带利率和干扰因素的双广义Poisson风险模型，模型中保费的收入和理赔都是广义Poisson过程，应用鞅论的方法，得到了破产概率的Lundberg不等式。

This paper studies the double generalized risk model with interest and diffusion . The premium income and the claim are a generalized Poisson process in this model . The Lundberg inequality of ruin probability is obtained by the method of martingale .

讨论了Jensen不等式在离散时间参数的鞅论中的应用，特别是在由已知鞅构造新的鞅中的应用。

In this paper , the author discuss the application of Jensen 's inequality in discrete time parametric martingale 's theories , especially for constructing some new martingales from the known one .

利用计数过程的理论和鞅论，得到了状态准备金的计算公式及其所满足的随机微分方程以及特定环境下的Thiele微分方程，从而计算出个人账户的退休金净赔偿率。

Using the theory of counting process and martingale , we get the formula of state reserve and its stochastic differential equation . Therefore the Thiele 's differential equation is obtained as well as the net indemnity rate of retirement from individual accounts .

而鞅论与停时更是现代金融学、破产理论、风险投资、保险学的理论基础。

Martingales and stopping times are the basis of Finance theory .

在现代鞅论中，鞅不等式具有很重要的作用。

Inequalities of martingales play an important role in modern martingale theory .

从而说明，鞅论是现代控制理论中一个重要工具，应该引起工程界的足够的重视。

The Martingale is a powerful tool in modern control theory research .

应用鞅论的方法，得出破产概率的一个不等式。

By using the method of Martingale , we get the inequality for the ultimately ruin probability .

鞅论是随机过程的一个前沿理论，近年来，它作为一个强有力的研究工具逐渐向各个学科渗透。

Martingale is a front theory in stochastic process , recently , it was gradually applied to various discipline .

其次介绍了随机分析的有关理论知识，特别是鞅论以及布朗运动等相关的随机分析知识。

Then the knowledge of stochastical analyse is considered , such as the thoery of martingale and Brown Motion , etc.

在第二章中，介绍了全文所涉及到的一些概念，以及更新理论知识和鞅论方法。

In the second chapter , it talks about some concepts mentioned in the whole paper and updates theories and martingale method .

在鞅论的发展过程中，鞅空间上的不等式一直是深受关注的研究热点。

In the course of the development of martingale theory , martingale space and inequalities have been a concerned research hot spot .

上个世纪七十年代以来鞅论的研究日渐活跃起来，其在理论和应用上的重要性也日益突出。

Since the early 1970 's , martingale has undergone a flourishing development , and become more and more important in theory and application .

首先，介绍了论文的研究背景，以及破产概率、随机过程、鞅论的基本知识。其次讨论连续型风险模型。

Then the basic theories about ruin probability 、 random process and martingale are also introduced . Secondly , discuss the continuous risk model .

所获结果为遗传算法的实际应用奠定了理论基础，且所使用的鞅论分析方法为遗传算法研究提供了全新的分析工具。

The obtained results underlies application of the GAs , and the suggested martingale analysis approach provides a new methodology for convergence analysis of genetic algorithms .

本论文即应用经典鞅论和随机点过程等理论研究分析了三类具有相依性结构的风险模型，得到了与破产相关的一些变量的表达式或性质。

In this text , the theory of classical martingale and stochastic point process are applied in studying three kinds of new risk models with dependence .

在鞅论中，原子分解的方法不仅可以处理小指标鞅空间，而且可以将单指标和多指标统一处理，在解决鞅空间对偶和内插理论中是简洁有效的。

In martingale theory , atomic decomposition methods not only deal with martingale spaces with small index , but also unify the single index and multiple index .

本论文利用更新理论、马氏过程、随机控制及鞅论等数学工具，主要研究了金融保险中几种风险过程的破产问题。

The paper investigate the ruin problem of several risk processes in finance and insurance by the renewal argument , Markov process , stochastic control and martingale theory .

并介绍了论文用到的基础知识，主要包括齐次泊松过程及其分解、风险理论、鞅论、效用理论的基本知识。

We mainly introduce the relevant knowledge about reinsurance . Then the basic theories about risk theory , random process , utility theory and martingale are also introduced .

本文旨在运用鞅论的方法研究随机神经网络的均方渐近稳定性、均方指数稳定性和自适应同步问题。

This dissertation aims to study the asymptotic stability in mean square , the exponential stability in mean square and the adaptive synchronization in pth moment for stochastic neural networks based on M-matrix approach .

新的模型下保险公司的盈余资本可用一个随机游动过程描述，利用停时理论和鞅论证明了保险公司的破产概率的一个上界。

In the new model , the surplus of the insurance company can be described by a random walk process . Based on the stopping-time theory and the martingale theory , an upper bound of the ruin probability is being proved .

从二十世纪六十年代后期开始，近代鞅论与随机分析理论蓬勃兴起，其中，鞅理论被用于研究随机点过程理论，在运用过程中显示出其独特的优越性。

Since the late 1960s , the modern martingale theory and theory of stochastic analysis has flourished . Among these the modern martingale theory has been applied to study the theory of stochastic point process and unique superiority has been shown in application .

本论文应用经典鞅论和随机点过程等理论研究分析了离散情形带常利率的泊松模型和双险种的二项风险模型，得到了与破产相关的一些重要变量的表达式或性质。

In this text , the theory of classical martingale and stochastic point process are applied in studying generalized poisson process whose premium is a stochastic process with constant interest force in discrete situation and the binomial risk model with double type insurance .

本学位论文主要致力于跳跃扩散模型的期权定价理论问题的研究，运用鞅论，随机分析等数学工具建立更一般跳跃扩散过程的期权定价数学模型，并推导出其定价公式以及平价关系。

This dissertation is intended to study option-pricing theory with jump-diffusion , so as to establish the mathematic module of option pricing with jump-diffusion process by means of mathematical tools such as martingale theory and stochastic analysis , and deduces the option pricing equation .

在无风险利率、指数连续股利率、指数瞬时波动率为时间t的非随机函数的情形下，以鞅论和随机分析为数学工具得到了重设型牛市认购权证的定价公式。

Under condition that the interest rate of the riskless asset , the volatility rate and the dividend rate of stock index are nonrandom functions of time , the pricing formula of bull market reset call warrants is obtained by using Martingale and stochastic analysis methods .

文中应用随机过程序列弱收敛，鞅以及概率论等理论，讨论了推广模型的伦德伯格不等式和最终破产概率公式，得出了和经典风险模型一样的结论。

By the method of martingale , we prove the Lundberg inequality and formula on the ruin probability .

然后利用鞅测度和概率论理论讨论了离散时间的上升敲出期权的二项式定价模型，并推导出其定价公式，此公式推广了标准的二项式定价公式；

By means of martingale method and the theory of probability , the binomial pricing model of discrete up-and-out calls is studied and the formula is deduced , which extends the binomial pricing model of the European option .